Problem: Simplify the expression. $(-3z^{2}-z)(-4z^{3}+6z^{2}+7z)$
Explanation: First use the distributive property. $ - 3 z^2 (-4 z^3) - 3 z^2 (6 z^2) - 3 z^2 (7 z) - z (-4 z^3) - z (6 z^2) - z (7 z) $ Simplify. $ 12z^{5} - 18z^{4} - 21z^{3} + 4z^{4} - 6z^{3} - 7z^{2} $ $12z^{5}-14z^{4}-27z^{3}-7z^{2}$ Identify like terms. $ { 12z^{5}} \color{#DF0030} {- 18z^{4}} {- 21z^{3}} \color{#DF0030} {+ 4z^{4}} {- 6z^{3}} {- 7z^{2}} $ Add the coefficients. $ { 12z^{5}} \color{#DF0030} { -14z^{4}} { -27z^{3}} { -7z^{2}} $